Question

prove that 2√13 is irrational​

Answer 1

Answer:

- Any number which is under a root and does not have a direct square root is irrational.

Here, we have 2√13, and √13 is not a direct square of any number, so 2√13 is irrational.

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Answer 2

Answer:Answer

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Ukumar1

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Let us assume that √13 is rational no and equals to p/q are Co primes

√13=p/q

squaring both sides

√13*2=p*2/q*2

13=p*2/q*2

13q*2=p*2

13/p*2

13/p

p=3r for some integer r

p*2=169r*2

13q*2=169*2

b*2=13r*2

13/b*2

13/b

13 is a common factor but this is contradiction hence our supposition is wrong √13 is irrational number

as we know multiplication of rational and irational number ios irrational

Therefore, 2root13 is irrational